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Competitive algorithms from competitive equilibria: nonclairvoyant scheduling under polyhedral constraints
 In Symposium on Theory of Computing, STOC 2014
"... We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding job ..."
Abstract

Cited by 5 (4 self)
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We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding jobs. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling. In this paper, we design nonclairvoyant online algorithms for PSP and its special cases – in this setting, the scheduler is unaware of the sizes of jobs. Our results are summarized as follows. • For minimizing total weighted completion time, we show a O(1)competitive algorithm. Surprisingly, we achieve this result by applying the wellknown Proportional Fairness algorithm (PF) to perform allocations each time instant. Though PF has been extensively studied in the context of maximizing fairness in resource allocation, we present the first analysis in adversarial and gen
EnergyEfficient Multiprocessor Scheduling for Flow Time and Makespan
 CoRR
"... Abstract: We consider energyefficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power sα when running at speed s, for α> 1. A scheduling algorithm needs to decide at any time both processor allocations and processor spee ..."
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Cited by 1 (1 self)
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Abstract: We consider energyefficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power sα when running at speed s, for α> 1. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with timevarying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelismclairvoyant (IPclairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an O(1)competitive algorithm, which significantly improves upon the best known nonclairvoyant algorithm. In the case of makespan plus energy, we present an O(ln1−1/α P)competitive algorithm, where P is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we also study nonclairvoyant scheduling for total flow time plus energy, and present an algorithm that achieves O(lnP)competitive for jobs with arbitrary release time and O(ln1/α P)competitive for jobs with identical release time. Finally, we prove an Ω(ln1/α P) lower bound on the competitive ratio of any nonclairvoyant algorithm.
Algorithms, Theory
"... We introduce a scheduling algorithm IntermediateSRPT, and show that it is O(logP)competitive with respect to average waiting time when scheduling jobs whose parallelizability is intermediate between being fully parallelizable and sequential. Here the parameter P denotes the ratio between the maxi ..."
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We introduce a scheduling algorithm IntermediateSRPT, and show that it is O(logP)competitive with respect to average waiting time when scheduling jobs whose parallelizability is intermediate between being fully parallelizable and sequential. Here the parameter P denotes the ratio between the maximum job size to the minimum. We also show a general matching lower bound on the competitive ratio. Our analysis builds on an interesting combination of potential function and local competitiveness arguments.